Nano-positioning is one of the foundations on which the modern nanotechnology is developed. High quality nano-positioning stages usually employ a close-loop feedback circuit in control electronics to ensure a desired position on a sub-nanometer (nm) scale. This requires position sensors, which directly measure the position of the stage. Several sensors are now commonly available for this purpose. For example, optical interferometers have been the standard for calibrating linear displacements, and are used in some translation stages as the position sensors. However, the relatively complex structure of this type of sensor makes it less desired in compact designs. Another mainstream nano-position sensors using direct metrology are gap-varying capacitive sensors with 0.01 nm resolution such as Physik Instrumente's gap-varying capacitive sensor (e.g., PI's D-015, D-050, and D-100 sensors). The resolution of this kind of capacitive sensor can out-perform high quality optical interferometers, and is believed to be the most sensitive position sensor in the marketplace. However, the physical design of this type of sensor is bulky due to the fact that the coupling area must be huge compared to the gap. Therefore, the dynamic range of this type of sensor is usually limited to at most a few hundred micrometers (μm).
Another disadvantage of gap-varying capacitive sensors (and perhaps of many other position sensors) is that the sensor response is not truly linear to the measured displacements. For example, Physik Instrumente's gap-varying capacitive sensors are gap-varying two-electrode capacitors. Consider the idealized approximation for the capacitance of parallel-plate capacitors, which is proportional to A/d, where A is the coupling area and d is the gap between the electrodes. Consequently, its capacitive response to the displacement, which causes “d” to vary, is nonlinear. The reason that Physik Instrumente's gap-varying capacitive sensors are able to claim linear responses is through a digital linearization algorithm, which means that the sensors are calibrated with polynomial approximations, and use the polynomial functions to digitally linearize the nonlinear capacitive responses.
In addition to the nonlinear capacitive response, since the sensors respond to the variation of the gap, the dynamic range is limited by the area. For longer travel distances, the area must be larger so that the polynomial approximations can be valid, and the area can not keep growing.
Efforts continue to develop nano-positioning sensors that do not have the problems associated with known nano-positioning sensors. In particular, efforts continue to develop nano-positioning sensors (i) having a sensor response that varies linearly to displacement of a sensor component, (ii) that can be made much smaller compared to known gap-varying capacitive sensors, and (iii) that can detect sub-nanometer displacements while having a potentially unlimited travel ranges for various applications.